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Nutation
Nutation () is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame it can be defined as a change in the second Euler angle. If it is not caused by forces external to the body, it is called ''free nutation'' or '' Euler nutation''. A ''pure nutation'' is a movement of a rotational axis such that the first Euler angle is constant. Therefore it can be seen that the circular red arrow in the diagram indicates the combined effects of precession and nutation, while nutation in the absence of precession would only change the tilt from vertical (second Euler angle). However, in spacecraft dynamics, precession (a change in the first Euler angle) is sometimes referred to as nutation. In a rigid body If a top is set at a tilt on a horizontal surface and spun rapidly, its rotational axis starts precessing about th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth's Rotation
Earth's rotation or Earth's spin is the rotation of planet Earth around its own Rotation around a fixed axis, axis, as well as changes in the orientation (geometry), orientation of the rotation axis in space. Earth rotates eastward, in retrograde and prograde motion, prograde motion. As viewed from the northern polar star Polaris, Earth turns counterclockwise. The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where Earth's axis of rotation meets its surface. This point is distinct from Earth's North Magnetic Pole. The South Pole is the other point where Earth's axis of rotation intersects its surface, in Antarctica. Earth rotates once in about 24 hours with respect to the Sun, but once every 23 hours, 56 minutes and 4 seconds with respect to other distant stars (#Stellar and sidereal day, see below). Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tida ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Angles
The Euler angles are three angles introduced by Leonhard Euler to describe the Orientation (geometry), orientation of a rigid body with respect to a fixed coordinate system.Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189–207 (E478PDF/ref> They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general Basis (linear algebra), basis in 3-dimensional linear algebra. Alternative forms were later introduced by Peter Guthrie Tait and George H. Bryan intended for use in aeronautics and engineering. Chained rotations equivalence Euler angles can be defined by elemental geometry or by composition of rotations. The geometrical definition demonstrates that three composed ''elemental rotations'' (rotations about the axes of a coordinate system) are always sufficient to reach any target frame. The three elemental rotations may be #Conventions by extrinsic rotations, extrinsic (rotations about the axes ''xyz'' of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called ''nutation''. In physics, there are two types of precession: torque-free and torque-induced. In astronomy, ''precession'' refers to any of several slow changes in an astronomical body's rotational or orbital parameters. An important example is the steady change in the orientation of the axis of rotation of the Earth, known as the precession of the equinoxes. Torque-free Torque-free precession implies that no external moment (torque) is applied to the body. In torque-free precession, the angular momentum is a constant, but the angular velocit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axial Precession
In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In particular, axial precession can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years.Hohenkerk, C.Y., Yallop, B.D., Smith, C.A., & Sinclair, A.T. "Celestial Reference Systems" in Seidelmann, P.K. (ed.) ''Explanatory Supplement to the Astronomical Almanac''. Sausalito: University Science Books. p. 99. This is similar to the precession of a spinning top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude. Earth's precession was historically called the precession of the equinoxes, because ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetic Energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. Formally, a kinetic energy is any term in a system's Lagrangian which includes a derivative with respect to time. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2. In relativistic mechanics, this is a good approximation only when ''v'' is much less than the speed of light. The standard unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound. History and etymology The adjective ''kinetic'' has its roots in the Greek word κίνησις ''kinesis'', m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Of Latitude
A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth (ignoring elevation) at a given latitude coordinate line. Circles of latitude are often called parallels because they are Parallel (geometry), parallel to each other; that is, planes that contain any of these circles never Intersection, intersect each other. A location's position along a circle of latitude is given by its longitude. Circles of latitude are unlike circles of longitude, which are all great circles with the centre of Earth in the middle, as the circles of latitude get smaller as the distance from the Equator increases. Their length can be calculated by a common sine or cosine function. The 60th parallel north or 60th parallel south, south is half as long as the Equator (disregarding Earth's minor flattening by 0.335%). On the Mercator projection or on the Gall-Peters projection, a circle of latitude is perpendicular to all meridian (geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ecliptic
The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system. Sun's apparent motion The ecliptic is the apparent path of the Sun throughout the course of a year. Because Earth takes one year to orbit the Sun, the apparent position of the Sun takes one year to make a complete circuit of the ecliptic. With slightly more than 365 days in one year, the Sun moves a little less than 1° eastward every day. This small difference in the Sun's position against the stars causes any particular spot on Earth's surface to catch up with (and stand directly north or south of) the Sun about four minutes later each day than it would if Earth did not orbit; a day on Earth is therefore 24 hours ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axial Tilt
In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbital plane. It differs from orbital inclination. At an obliquity of 0 degrees, the two axes point in the same direction; that is, the rotational axis is perpendicular to the orbital plane. The rotational axis of Earth, for example, is the imaginary line that passes through both the North Pole and South Pole, whereas the Earth's orbital axis is the line perpendicular to the imaginary plane through which the Earth moves as it revolves around the Sun; the Earth's obliquity or axial tilt is the angle between these two lines. Earth's obliquity oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle. Based on a continuously updated formula (here Laskar, 1986, though since 2006 the IMCCE and the IAU recommend the P03 model), Earth's mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trópico De Cáncer En México - Carretera 83 (Vía Corta) Zaragoza-Victoria, Km 27+800
Trópico (Spanish and Portuguese for ‘tropic’) or Tropico may refer to: Computing * ''Tropico'' (video game), a 2001 construction simulation game *Tropicos, an online botanical database Film and television * ''Tropico'' (film), a 2013 American short film featuring Lana Del Rey * ''Trópico'' (TV series), a 2007 Venezuelan-Dominican telenovela Music * ''Tropico'' (Pat Benatar album), 1984 * ''Trópico'' (Ricardo Arjona album), 2009 *''Tropico'', an album by Gato Barbieri, 1978 *''Tropico'', an album by Tony Esposito Anthony James "Tony O" Esposito (April 23, 1943 – August 10, 2021) was a Canadian-American professional ice hockey goaltender, who played 16 seasons in the National Hockey League (NHL), 15 of those for the Chicago Black Hawks. He was one of t ..., 1996 Places * Trópico (Bolivia), a subdivision of Cochabamba, Bolivia {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Bradley
James Bradley (1692–1762) was an English astronomer and priest who served as the third Astronomer Royal from 1742. He is best known for two fundamental discoveries in astronomy, the aberration of light (1725–1728), and the nutation of the Earth's axis (1728–1748). These two discoveries were called "the most brilliant and useful of the century" by Jean Baptiste Joseph Delambre, historian of astronomy, mathematical astronomer and director of the Paris Observatory. In his ''History of astronomy in the 18th century'' (1821), Delambre stated:"It is to these two discoveries by Bradley that we owe the exactness of modern astronomy. ... This double service assures to their discoverer the most distinguished place (after Hipparchus and Kepler) above the greatest astronomers of all ages and all countries." Biography Bradley was born at Sherborne, near Cheltenham in Gloucestershire, to William Bradley and Jane Pound in September 1692. His nephew John was also an astronomer. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Derivative
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t. Notation A variety of notations are used to denote the time derivative. In addition to the normal ( Leibniz's) notation, :\frac A very common short-hand notation used, especially in physics, is the 'over-dot'. I.E. :\dot (This is called Newton's notation) Higher time derivatives are also used: the second derivative with respect to time is written as :\frac with the corresponding shorthand of \ddot. As a generalization, the time derivative of a vector, say: : \mathbf v = \left v_1,\ v_2,\ v_3, \ldots \right is defined as the vector whose components are the derivatives of the components of the original vector. That is, : \frac = \left \frac,\frac ,\frac , \ldots \right . Use in physics Time derivatives are a key concept in physics. For example, for a changing position x, its t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
